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A074294
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Integers 1 to 2*k followed by integers 1 to 2*k + 2 and so on.
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6
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1, 2, 1, 2, 3, 4, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 7, 8, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 1, 2
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Comment from Cino Hilliard (hillcino368(AT)gmail.com), Sep 13 2004: "Also the numerator of the fraction in the continued fraction expansion of sqrt(n) for nonsquare n = 2,3,5,6,7... . E.g. for n = 7,
"sqrt(7).=.2.+._3_................
"...............4..+._3_..........
".....................4..+._3_....
"...........................4.....
"3 is the 5th entry in the table. sqrt(1) and sqrt(4) are not included because 1 and 4 are squares."
A074294 is the natural fractal sequence of A002061; the corresponding natural interspersion is A194011; see A194029 for definitions. [From Clark Kimberling, Aug 17 2011]
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FORMULA
| a(n^2 + n) = 2*n.
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MATHEMATICA
| A074294[n_] := n - 2*Binomial[Floor[1/2 + Sqrt[n]], 2] [From E. Perez Herrero (psychgeometry(AT)gmail.com), Apr 14 2010]
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PROG
| (PARI) {a(n) = n - 2 * binomial( floor( 1/2 + sqrt(n)), 2)}
(PARI) gp > c(n) = for(x=2, n, if(issquare(x)==0, a=floor(sqrt(x)); print1(x-a^2", "))) (Cino Hilliard)
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CROSSREFS
| Cf. A002061, A194011.
Sequence in context: A194865 A075425 A194103 * A168265 A062050 A169778
Adjacent sequences: A074291 A074292 A074293 * A074295 A074296 A074297
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KEYWORD
| nonn,easy
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AUTHOR
| Michael Somos, Aug 20 2002
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